ssume that X has a normal distribution. ind the probability that X is greater than
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
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![### Understanding Normal Distribution
Understanding how to use the normal distribution is an essential skill in statistics. Given the characteristics of a dataset, you can determine the likelihood of a particular outcome. Let's explore this concept further using an example.
### Example Question
Assume that \( X \) has a normal distribution. The mean is \( \mu = 15.2 \) and the standard deviation is \( \sigma = 0.9 \).
#### Problem:
Find the probability that \( X \) is greater than 15.2.
To find this probability, you can use the Z-table. The Z-table helps you understand the proportion of values to the left of a given Z-score in a standard normal distribution.
Here's the question and the options:
1. Click to view page 1 of the table. Click to view page 2 of the table.
#### Select the correct option:
- A. 1.0000
- B. 0.9998
- C. 0.0003
- D. 0.5000
### Steps to Solve:
1. **Identify the given data:**
- Mean (\(\mu\)) = 15.2
- Standard Deviation (\(\sigma\)) = 0.9
2. **Calculate the Z-score:**
The Z-score formula is:
\[
Z = \frac{(X - \mu)}{\sigma}
\]
Here, since we are finding \( P(X > 15.2) \):
\[
Z = \frac{(15.2 - 15.2)}{0.9} = 0
\]
3. **Find the probability:**
Use the Z-table to find the probability corresponding to the Z-score.
For \( Z = 0 \), the Z-table shows that 50% of the values lie to the left of \( Z = 0 \).
Therefore, \( P(X > 15.2) \) is the remaining 50%, since it’s a symmetric distribution.
So, the probability:
\[
P(X > 15.2) = 0.5000
\]
### Final Answer:
- D. 0.5000
Understanding how to work with the normal distribution and use the Z-table is crucial for solving such problems. It is a fundamental concept used across various fields such](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F4b33feb0-e62b-4e25-aad1-2d23e491b0f1%2Fd2e31d02-491a-42ee-a53a-43994c913ba3%2Fhgy4qfe_processed.png&w=3840&q=75)
Transcribed Image Text:### Understanding Normal Distribution
Understanding how to use the normal distribution is an essential skill in statistics. Given the characteristics of a dataset, you can determine the likelihood of a particular outcome. Let's explore this concept further using an example.
### Example Question
Assume that \( X \) has a normal distribution. The mean is \( \mu = 15.2 \) and the standard deviation is \( \sigma = 0.9 \).
#### Problem:
Find the probability that \( X \) is greater than 15.2.
To find this probability, you can use the Z-table. The Z-table helps you understand the proportion of values to the left of a given Z-score in a standard normal distribution.
Here's the question and the options:
1. Click to view page 1 of the table. Click to view page 2 of the table.
#### Select the correct option:
- A. 1.0000
- B. 0.9998
- C. 0.0003
- D. 0.5000
### Steps to Solve:
1. **Identify the given data:**
- Mean (\(\mu\)) = 15.2
- Standard Deviation (\(\sigma\)) = 0.9
2. **Calculate the Z-score:**
The Z-score formula is:
\[
Z = \frac{(X - \mu)}{\sigma}
\]
Here, since we are finding \( P(X > 15.2) \):
\[
Z = \frac{(15.2 - 15.2)}{0.9} = 0
\]
3. **Find the probability:**
Use the Z-table to find the probability corresponding to the Z-score.
For \( Z = 0 \), the Z-table shows that 50% of the values lie to the left of \( Z = 0 \).
Therefore, \( P(X > 15.2) \) is the remaining 50%, since it’s a symmetric distribution.
So, the probability:
\[
P(X > 15.2) = 0.5000
\]
### Final Answer:
- D. 0.5000
Understanding how to work with the normal distribution and use the Z-table is crucial for solving such problems. It is a fundamental concept used across various fields such
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